- Source: Absolutely maximally entangled state
The absolutely maximally entangled (AME) state is a concept in quantum information science, which has many applications in quantum error-correcting code, discrete AdS/CFT correspondence, AdS/CMT correspondence, and more. It is the multipartite generalization of the bipartite maximally entangled state.
Definition
The bipartite maximally entangled state
|
ψ
⟩
A
B
{\displaystyle |\psi \rangle _{AB}}
is the one for which the reduced density operators are maximally mixed, i.e.,
ρ
A
=
ρ
B
=
I
/
d
{\displaystyle \rho _{A}=\rho _{B}=I/d}
. Typical examples are Bell states.
A multipartite state
|
ψ
⟩
{\displaystyle |\psi \rangle }
of a system
S
{\displaystyle S}
is called absolutely maximally entangled if for any bipartition
A
|
B
{\displaystyle A|B}
of
S
{\displaystyle S}
, the reduced density operator is maximally mixed
ρ
A
=
ρ
B
=
I
/
d
{\displaystyle \rho _{A}=\rho _{B}=I/d}
, where
d
=
min
{
d
A
,
d
B
}
{\displaystyle d=\min\{d_{A},d_{B}\}}
.
Property
The AME state does not always exist; in some given local dimension and number of parties, there is no AME state. There is a list of AME states in low dimensions created by Huber and Wyderka.
The existence of the AME state can be transformed into the existence of the solution for a specific quantum marginal problem.
The AME can also be used to build a kind of quantum error-correcting code called holographic error-correcting code.